Unsigned interpretation of a bit string ($\mathrm{bin}(A)={\sum }_{i=0}^{n-1}{a}_i{2}^i$)

For an $n$-bit binary string $A=a_{n-1}\cdots a_0$, the unsigned interpretation assigns positive positional weights $2^i$ to its bits. Its values range from zero to $2^n-1$. The same stored bits have two's complement value $\mathrm{bin}(A)-a_{n-1}{2}^n$, so interpreting a machine word is a separate choice from storing its bits.